These differences could develop because, if one assumes that a topological space satisfies the T1 axiom, then the various definitions are (in most cases) equivalent.
But if one did not make that assumption, then the simplest definition might not be the right one for the most useful concept; in any case, it would destroy the (transitive) entailment of Ti by Tj, allowing (for example) non-Hausdorff regular spaces.
Topologists working on the metrisation problem generally did assume T1; after all, all metric spaces are T1.
Then, for those occasions when they did not assume T1, they used words ("regular" and "normal") for the more complicated definitions, in order to contrast them with the simpler ones.
This approach was used as late as 1970 with the publication of Counterexamples in Topology by Lynn A. Steen and J. Arthur Seebach, Jr.
Since 1970, the general topologists' terms have been growing in popularity, including in other branches of mathematics, such as analysis.